The world wide use of teleprinter technology necessitates teleprinters for many different types of script. Thus, teleprinters are known for Latin and for Arabic script. However, situations also occur which require the common use of teleprinters for different scripts. In this case, both teleprinters must be able to be connected to the teleprinter network via a common connection line and this connection is to be carried out selectively in order to facilitate a connection to the one or to the other teleprinter. It is known to provide devices which are referred to as so-called remote switching devices or recently so-called remote switching units to connect teleprinters to the connection line which leads to the actual exchange. A known remote switching unit (German AS 2 36 635) comprises a control component and a line matching component. The control component can assume the functions of known remote switching devices. In the line matching component on the one hand the states prevailing on the connection line are evaluated to form criteria which are forwarded to the control component; on the other hand, as a result of the evaluation of the criteria formed in the control component, the states on the connection line are changed. Although a remote switching unit of this kind advantageously permits adaptation to many different processes of transmission on the connection line and the connected terminal devices are themselves not subject to any special requirements, this known arrangement is not suitable for the connection of a plurality of terminal devices to which random access is to be provided. The quoted AS 2 36 635 does, in fact, disclose a possibility of connecting an additional device, but this arrangement only permits monitoring operation.